Formula used
A midpoint lies halfway between two endpoints. Average matching coordinates to locate it. The same principle works across every supported coordinate dimension.
| Calculation | Formula | Purpose |
|---|---|---|
| 1D midpoint | M = (x₁ + x₂) / 2 | Finds the centre between two numbers. |
| 2D midpoint | M = ((x₁+x₂)/2, (y₁+y₂)/2) | Finds a segment centre on a plane. |
| 3D midpoint | M = ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2) | Finds a centre in three-dimensional space. |
| Missing endpoint | x₂ = 2xₘ − x₁, y₂ = 2yₘ − y₁ | Reconstructs an unknown endpoint. |
| Ratio point | P = ((nx₁+mx₂)/(m+n), (ny₁+my₂)/(m+n)) | Divides a segment internally. |
How to use this calculator
Select the calculation mode first. Enter coordinates using decimals, fractions, or scientific notation. Then choose precision and press the calculate button.
- Choose midpoint, endpoint, ratio, weighted, multiple, or geographic mode.
- Enter every required coordinate and optional ratio or weight.
- Select your preferred precision and display format.
- Review the result, formula, steps, distances, and graph.
- Copy or download the result when needed.
Example data
These examples demonstrate common midpoint tasks. Each row can be loaded manually. Results include exact and rounded coordinate forms.
| Mode | Inputs | Expected result |
|---|---|---|
| 2D midpoint | A(2, 4), B(8, 10) | M(5, 7) |
| 3D midpoint | A(2, 4, 1), B(8, 10, 9) | M(5, 7, 5) |
| Missing endpoint | A(2, 4), M(5, 7) | B(8, 10) |
| Ratio point | A(0, 0), B(12, 6), ratio 1:2 | P(4, 2) |
| Multiple points | (2,4), (8,10), (5,1) | C(5, 5) |
Common mistakes
Coordinate order must remain consistent. Average x-values together and y-values together. Never divide only one coordinate sum by two.
- Do not confuse midpoint distance with full segment distance.
- Keep latitude before longitude in geographic mode.
- Use positive ratio values for internal segment division.
- Remember that larger weights pull the centre closer.
Frequently asked questions
What is a midpoint?
A midpoint is a segment’s exact centre. It divides the segment into equal lengths. Both endpoints remain equally distant from the midpoint.
Can the calculator use negative coordinates?
Yes, negative coordinates are fully supported. They may place points in different quadrants. The graph scales automatically around all entered points.
Can I enter fractions?
Yes, enter values like 3/4 or -5/2. Decimal and scientific notation also work. Exact fractional results appear whenever they are meaningful.
How is a missing endpoint calculated?
Double each midpoint coordinate first. Then subtract the known endpoint coordinate. This reverses the standard midpoint averaging process exactly.
What does a ratio point mean?
A ratio point divides a segment internally. The two ratio numbers control relative lengths. Equal ratio values produce the ordinary midpoint location.
What is a weighted midpoint?
A weighted midpoint considers unequal point importance. Larger weights pull the result closer. Equal weights produce the ordinary midpoint between points.
Does geographic midpoint mean average latitude and longitude?
Not always, because Earth is approximately spherical. This tool averages spherical direction vectors instead. That method handles long distances more reliably.
Why are both exact and decimal results shown?
Exact fractions preserve mathematical precision. Decimals are often easier to interpret. Showing both formats supports checking and practical application.
Can I download my calculation?
Yes, results can be copied or downloaded. CSV works well for spreadsheets. PDF provides a convenient formatted calculation record.